Solving the Steiner Tree Problem in Graphs with Chaotic Neural Networks: A Nonlinear Time Series Analysis of the Objective Function Value

Chaotic neural networks (ChNNs) provide an effective method to solve combinatorial optimization problems, because their chaotic behavior is considered to encourage smooth escape from local optima. However, whether ChNN models exhibit chaotic behavior when searching for solutions remains unknown, which means there may be other reasons for their good performance. From this perspective, we analyzed the deterministic features of a chaotic time series from the transition of the objective function value. The results obtained by the E1, IDNP, and R series indicate that the transitions of the objective function value for solving the Steiner tree problem in graphs exhibited weak determinism, similar to that of the transition of a chaotic neuron’s internal state in a plain ChNN.